## Journals

- Advances in Mathematics of Communications
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DCDS-B

In this paper we deal with diffusive relaxation limits of
nonlinear systems of Euler type modeling chemotactic movement of
cells toward Keller-Segel type systems. The approximating systems
are either hyperbolic-parabolic or hyperbolic-elliptic. They all
feature a nonlinear pressure term arising from a

*volume filling effect*which takes into account the fact that cells do not interpenetrate. The main convergence result relies on energy methods and compensated compactness tools and is obtained for large initial data under suitable assumptions on the approximating solutions. In order to justify such assumptions, we also prove an existence result for initial data which are small perturbation of a constant state. Such result is proven via classical Friedrichs's symmetrization and linearization. In order to simplify the coverage, we restrict to the two-dimensional case with periodical boundary conditions.
CPAA

This paper deals with the rigorous study of the diffusive stress relaxation in
the multidimensional system arising in the mathematical modeling of
viscoelastic materials. The control of an appropriate high order
energy shall lead to the proof of that limit in Sobolev space. It is
shown also as the
same result can be obtained in terms of relative modulate energies.

DCDS-B

We study the low Mach number limit for the compressible
Navier-Stokes system supplemented with Navier's boundary condition
on an unbounded domain with compact boundary. Our main result
asserts that the velocities converge pointwise to a solenoidal
vector field - a weak solution of the incompressible Navier-Stokes
system - while the fluid density becomes constant. The proof is
based on a variant of local energy decay property for the underlying
acoustic equation established by Kato.

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